Painl\'eve III and a singular linear statistics in Hermitian random matrix ensembles I

In this paper, we study a certain linear statistics of the unitary Laguerre ensembles, motivated in part by an integrable quantum field theory at finite temperature. It transpires that this is equivalent to the characterization of a sequence of polynomials orthogonal with respect to the weight w(x)=w(x,s):=x^{\al}\rme^{-x}\rme^{-s/x}, \quad 0\leq x0, s>0, namely, the determination of the associated Hankel determinant and recurrence coefficients. Here $w(x,s)$ is the Laguerre weight x^{\al}\:\rme^{-x} 'perturbed' by a multiplicative factor \rme^{-s/x}, which induces an infinitely strong zero at the origin. For polynomials orthogonal on the unit circle, a particular example where there are explicit formulas, the weight of which has infinitely strong zeros, was investigated by Pollazcek and Szeg\"o many years ago. Such weights are said to be 'singular' or irregular due to the violation of the Szeg\"o condition. In our problem, the linear statistics is a sum of the reciprocal of positive random variables $\{x_j:j=1,..,,n\};$ $\sum_{j=1}^{n}1/x_j.$ We show that the moment generating function, or the Laplace transform of the probability density function of this linear statistics is expressed as the ratio of Hankel determinants and as an integral of the combination of a particular third Painlev\'e function.Comment: 29 page

The real-time learning mechanism of the Scientific Research Associates Advanced Robotic System (SRAARS)

Scientific research associates advanced robotic system (SRAARS) is an intelligent robotic system which has autonomous learning capability in geometric reasoning. The system is equipped with one global intelligence center (GIC) and eight local intelligence centers (LICs). It controls mainly sixteen links with fourteen active joints, which constitute two articulated arms, an extensible lower body, a vision system with two CCD cameras and a mobile base. The on-board knowledge-based system supports the learning controller with model representations of both the robot and the working environment. By consecutive verifying and planning procedures, hypothesis-and-test routines and learning-by-analogy paradigm, the system would autonomously build up its own understanding of the relationship between itself (i.e., the robot) and the focused environment for the purposes of collision avoidance, motion analysis and object manipulation. The intelligence of SRAARS presents a valuable technical advantage to implement robotic systems for space exploration and space station operations

Video Captioning with Guidance of Multimodal Latent Topics

The topic diversity of open-domain videos leads to various vocabularies and linguistic expressions in describing video contents, and therefore, makes the video captioning task even more challenging. In this paper, we propose an unified caption framework, M&M TGM, which mines multimodal topics in unsupervised fashion from data and guides the caption decoder with these topics. Compared to pre-defined topics, the mined multimodal topics are more semantically and visually coherent and can reflect the topic distribution of videos better. We formulate the topic-aware caption generation as a multi-task learning problem, in which we add a parallel task, topic prediction, in addition to the caption task. For the topic prediction task, we use the mined topics as the teacher to train a student topic prediction model, which learns to predict the latent topics from multimodal contents of videos. The topic prediction provides intermediate supervision to the learning process. As for the caption task, we propose a novel topic-aware decoder to generate more accurate and detailed video descriptions with the guidance from latent topics. The entire learning procedure is end-to-end and it optimizes both tasks simultaneously. The results from extensive experiments conducted on the MSR-VTT and Youtube2Text datasets demonstrate the effectiveness of our proposed model. M&M TGM not only outperforms prior state-of-the-art methods on multiple evaluation metrics and on both benchmark datasets, but also achieves better generalization ability.Comment: ACM Multimedia 201